Generalised Wishart Processes
Andrew Wilson, Zoubin Ghahramani
We introduce a new stochastic process called the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary input variable. We use this process as a prior over dynamic (e.g. time varying) covariance matrices. The GWP captures a diverse class of covariance dynamics, naturally handles missing data, scales nicely with dimension, has easily interpretable parameters, and can use input variables that include covariates other than time. We describe how to construct the GWP, introduce general procedures for inference and prediction, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH.
PDF Link: /papers/11/p736-wilson.pdf
AUTHOR = "Andrew Wilson
and Zoubin Ghahramani",
TITLE = "Generalised Wishart Processes",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "736--744"